# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a003598
Showing 1-1 of 1

%I A003598 #47 Sep 08 2022 08:44:32
%S A003598 1,5,11,25,55,121,125,275,605,625,1331,1375,3025,3125,6655,6875,14641,
%T A003598 15125,15625,33275,34375,73205,75625,78125,161051,166375,171875,
%U A003598 366025,378125,390625,805255,831875,859375,1771561,1830125,1890625
%N A003598 Numbers of the form 5^i * 11^j.
%H A003598 Reinhard Zumkeller, <a href="/A003598/b003598.txt">Table of n, a(n) for n = 1..10000</a>
%F A003598 An asymptotic formula for a(n) is roughly 1/sqrt(55)*exp(sqrt(2*log(5)*log(11)*n)). - _Benoit Cloitre_, Mar 08 2002
%F A003598 The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(55*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - _Peter Bala_, Mar 18 2019
%F A003598 Sum_{n>=1} 1/a(n) = (5*11)/((5-1)*(11-1)) = 11/8. - _Amiram Eldar_, Sep 23 2020
%F A003598 a(n) ~ exp(sqrt(2*log(5)*log(11)*n)) / sqrt(55). - _Vaclav Kotesovec_, Sep 23 2020
%t A003598 Take[Union[(5^#[[1]] 11^#[[2]])&/@Tuples[Range[0,20],{2}]],50]  (* _Harvey P. Dale_, Dec 26 2010 *)
%t A003598 fQ[n_]:=PowerMod[55, n, n] == 0; Select[Range[2*10^6], fQ] (* _Vincenzo Librandi_, Jun 27 2016 *)
%o A003598 (PARI) list(lim)=my(v=List(),N);for(n=0,log(lim)\log(11),N=11^n;while(N<=lim,listput(v,N);N*=5));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jun 28 2011
%o A003598 (Haskell)
%o A003598 import Data.Set (singleton, deleteFindMin, insert)
%o A003598 a003598 n = a003598_list !! (n-1)
%o A003598 a003598_list = f $ singleton (1,0,0) where
%o A003598    f s = y : f (insert (5 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
%o A003598          where ((y, i, j), s') = deleteFindMin s
%o A003598 -- _Reinhard Zumkeller_, May 15 2015
%o A003598 (Magma) [n: n in [1..2*10^6] | PrimeDivisors(n) subset [5, 11]]; // _Vincenzo Librandi_, Jun 27 2016
%o A003598 (GAP) Filtered([1..2*10^6],n->PowerMod(55,n,n)=0); # _Muniru A Asiru_, Mar 19 2019
%o A003598 (Sage)
%o A003598 [n for n in (1..2*10^6) if n%55 in {0, 1, 5, 11, 15, 20, 25, 45} and all(x in {5,11} for x in prime_factors(n))] # _F. Chapoton_, Mar 16 2020
%Y A003598 Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A108698, A003599, A107788, A108687, A108779, A108090.
%K A003598 nonn,easy
%O A003598 1,2
%A A003598 _N. J. A. Sloane_

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE